On the Converse of the Theory of Groups Acting on Trees with Inversions

In this paper we show that if G is a group acting on a graph X with inversions such that G has a presentation induced by a fundamental domain for the action of G on X, then X is a tree. Received: January 3, 2007., Revised: August 10, 2007 and May 3, 2008., Accepted: October 17, 2008.